Beyond LATE: Identification of ATEs of Always-Takers and Never-Takers

• In Event: Causal Inference: Accounting For Heterogeneity

Abstract

In the presence of heterogeneous treatment effects, instrumental variable (IV) estimation only point identifies the local average treatment effect (LATE). The LATE is an average treatment effect (ATE) for a subpopulation whose treatment taking decision can be shifted by the instrument. Hence, LATE is often criticized for limited external validity. To address the limited external validity of LATE, this paper provides a set of identification results necessary to extrapolate the LATE to the ATEs of always-takers and never-takers. We first show that the ATEs of always-takers and never-takers can be written as the weighted average of marginal treatment effect (MTE) functions. We then demonstrate that, under further parametric assumptions on the MTE function, we can point identify the ATEs of always-takers and never-takers. Furthermore, we show in the absence of these parametric assumptions, we can nonetheless construct the bounds of the ATEs of always-takers and never-takers. We prove that the linear programming method developed by Mogstad et al. (2018) provides bounds that improve in terms of interpretability and performance over alternatives, including bounding the support of the outcome variable, requiring monotonicity or smoothness in the treatment response. A simulation study and an application based on Kern and Hainmueller (2009) are provided to illustrate the proposed methodology.

Authors

• Robert Gulotty, The University of Chicago

• Arthur Zeyang Yu, University of Chicago